Dorothy Sayers is clear on the need to do some memorization during the Grammar stage. Here is the next excerpt from her essay, "The Lost Tools of Learning":
During this age we must, of course, exercise the mind on other things besides Latin grammar. Observation and memory are the faculties most lively at this period; and if we are to learn a contemporary foreign language we should begin now, before the facial and mental muscles become rebellious to strange intonations. Spoken French or German can be practiced alongside the grammatical discipline of the Latin.
In English, meanwhile, verse and prose can be learned by heart, and the pupil's memory should be stored with stories of every kind--classical myth, European legend, and so forth. I do not think that the classical stories and masterpieces of ancient literature should be made the vile bodies on which to practice the techniques of Grammar--that was a fault of mediaeval education which we need not perpetuate. The stories can be enjoyed and remembered in English, and related to their origin at a subsequent stage. Recitation aloud should be practiced, individually or in chorus; for we must not forget that we are laying the groundwork for Disputation and Rhetoric.
Thanks to Susan Wise Bauer's First Language Lessons curriculum, I finally started doing serious memorization work with my daughter. She has memorized two poems so far and seems to enjoy the process of memorizing almost as much as her feeling of accomplishment from having successfully learned the poems. Bauer makes memorizing almost easy in her First Language Lessons. She introduces the poem, does a little dictation exercise from it, and has the teacher read it aloud 3 times a day or so for a couple of weeks, eventually having the student recite longer and longer portions of the poem together with the teacher. My daughter does well with this method, and my fears about imposing detested memorization work on my daughter have been put to rest. Clearly I am the one with the issues about memorization, not she.
As to the other things mentioned in this excerpt, we are raising our children to be bilingual in English and German, and we surround them with all sorts of enticing library books full of "stories of every kind". One of the best parts of homeschooling for us is that the children have so much time to read and love those books.